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Fully relativistic pseudopotentials

Fully relativistic pseudopotentials generated by
the MBK (PRB 47, 6728 (1993)) scheme within LDA (CA19) and GGA (PBE19) which contain
a partial core correction and fully relativistic effects including spin-orbit coupling.

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Pseudo-atomic orbitals

The number below the symbol means a cutoff radius (a.u.) of the confinement
potential. These file includes fifteen radial parts for each angular
momentum quantum number l (=0,1,2,3). The basis functions were generated by variationally
optimizing the corresponding primitive basis functions in the single atom.
The input files used for the orbital optimization can be found at
Bi_opt.dat .
Since Bi_CA19.vps and Bi_PBE19.vps include the 5d, 6s, and 6p states (15 electrons)
as the valence states, the minimal basis set is Bi*.*-s1p1d1.
Our recommendation for the choice of cutoff radius of basis functions is that
Bi8.0.pao is enough for bulks, but Bi10.0.pao or Bi12.0.pao is preferable
for molecular systems.

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Benchmark calculations by the PBE19 pseudopotential with the various basis functions

**(1) Calculation of the total energy as a function of lattice constant in the fcc structure,**
where the total energy is plotted relative to the minimum energy for each case. a_{0}
and B_{0} are the equilibrium lattice constant and bulk modulus obtained by fitting to
the Murnaghan equation of state. The difference between Bi8.0-s3p3d3f2 and Bi8.0-s4p4d3f2
in the total energy at the minimum point is 0.0033 eV/atom.
An input file used for the OpenMX calculations can be found at
Bifcc-EvsV.dat .
For comparison the result by the Wien2k code is also shown, where
the calculation was performed by default setting in the Ver. 10.1 of Wien2k except for
the use of R_{MT} x K_{MAX} of 12.

**(2) Calculations of the band dispersion in the fcc structure,**
where the non-spin polarized collinear calculation with the lattice constant of 5.06 Ang.
was performed using Bi_PBE19.vps and Bi8.0-s3p3d3f2 and the origin of the energy
is taken to be the Fermi level.
The input file used for the OpenMX calculations can be found at
Bifcc-Band.dat .
For comparison the result by the Wien2k code is also shown, where
the calculation was performed by default setting in the Ver. 10.1 of Wien2k
except for the use of R_{MT} x K_{MAX} of 12.